A couple of thoughts:
1. I was in your boat, but have gone from nothing in March of this year, to 2nd author on a submitted paper to American Journal of Sports Med and 1st author on a manuscript nearing completion for Journal of Trauma-- it definately can be done, but you have to be your own advocate and also have some time or light rotations to devote to the research.
2. People might argue with me on this, but I think some research, even non-ortho, is better than none. Especially research which lands you a finished product (peer reviewed journal article, conference poster or presentation, etc.). It separates you from all of the applicants that have "research" but haven't seen a project to completion.
3. Many programs have a senior resident at any given time on a multi-month research block as part of their residency curriculum. That resident at your school might be the most approachable, available, and best option for you, especially now. They frequently need help.
4. You may approach a faculty member you trust and offer to work on an IRB proposal for a project they have been thinking about but just havent started. It will be a great research experience just to learn that process, and you can then get in on the ground floor of a project that way. Many places have administrators and instruction packets to guide you through the process...
Don't sweat it. The best thing you can do in third year is rock your clerkships. Try to make the research happen, but not at the expense of anything else.
Good luck. Feel free to PM with specific questions.